Nicole, Zoe and Ivory have equal number of erasers. Nicole packs all her erasers equally into 8 packets. Zoe packs all her erasers equally into 7 packets. Ivory packs all her erasers equally into 4 packets. 6 packets of Nicole's erasers, 5 packets of Zoe's erasers and 2 packets of Ivory's erasers add up to 440 erasers. How many erasers do they have altogether?

	Nicole	Zoe	Ivory
Number of packets	8	7	4
Number of erasers	56 u	56 u	56 u
Number of erasers in each packet	7 u	8 u	14 u

All the erasers can be put into the packets without remainder.

All the children have equal numbers of erasers. 
Make the number of erasers that each child has the same. LCM of 8, 7 and 4 = 56

Number of erasers that each child has = 56 u

Number of erasers in 1 packet of Nicole's erasers = 56 u ÷ 8 = 7 u
Number of erasers in 1 packet of Zoe's erasers = 56 u ÷ 7 = 8 u
Number of erasers in 1 packet of Ivory's erasers = 56 u ÷ 4 = 14 u

Number of erasers in 6 packets of Nicole's erasers, 5 packets of Zoe's erasers and 2 packets of Ivory's erasers
= (6 x 7 u) + (5 x 8 u) + (2 x 14 u)
= 42 u + 40 u + 28 u
= 110 u

110 u = 440

1 u = 440 ÷ 110 = 4

Total number of erasers that they have
= 3 x 56 u
= 168 u
= 168 x 4
= 672

Answer(s): 672